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Manny Rayner's book reviews

I love reviewing books - have been doing it at Goodreads, but considering moving here.

Currently reading

The Greatest Show On Earth: The Evidence For Evolution
Richard Dawkins
R in Action
Robert Kabacoff
Fluid Concepts and Creative Analogies
Douglas R. Hofstadter
McGee on Food and Cooking: An Encyclopedia of Kitchen Science, History and Culture
Harold McGee
Epistemic Dimensions of Personhood
Simon Evnine
Pattern Recognition and Machine Learning (Information Science and Statistics)
Christopher M. Bishop
Relativity, Thermodynamics and Cosmology
Richard C. Tolman
The Cambridge Handbook of Second Language Acquisition
Julia Herschensohn, Martha Young-Scholten

Mathematics and Humor

Mathematics and Humor: A Study of the Logic of Humor - John Allen Paulos I've always felt that one of the really big philosophical questions concerns the nature of humour. What is humour? What purpose, if any, does it serve? Why are some things funny, and others not? I've thought about this stuff, on and off, for ages. The other day, I was poking around on Google and stumbled over this little book, which I immediately ordered from Amazon. It arrived yesterday and only took an evening to read.

Well... if you've got a mathematical background and you're as interested as I am in these issues, I strongly recommend it. The author starts by giving you a quick tour through various theories of humour, from antiquity to the present day. Lots of eminent thinkers have had something to say here: Plato, Hobbes, Kant, Hazlitt, Schopenhauer and Bergson all get quoted. There is a great deal of diversity, but one theme that keeps coming back is incongruity. Humour arises when two radically different ways of looking at something are juxtaposed. Though, as the author immediately notes, incongruity isn't enough on its own. There needs to be a point, and timing is very important. This is all lead-up to his own theory, whose immediate predecessor is Koestler, in The Act of Creation. Koestler argues that humour and creativity are closely linked: the patterns of thought are similar in both cases, though the end result is different.

The next few chapters build up the necessary mathematical and logical background, and if you know a little about logic you'll find them straightforward. He tells you about formal theories and models, and how a formal theory can have models that are very different. He also talks about self-reference and grammar, though I found this part a bit of a detour. The grammar is necessary though when he wants to discuss puns and plays on words.

Finally, he gets to the point, and a very imaginative one it is too! He suggests that catastrophe theory might give you a mathematical tool that lets you understand humour. The idea isn't as far-fetched as it may sound. Catastrophe theory, which he introduces in a simple and non-technical way, is about discontinuous change in dynamic systems, where the system suddenly flips over to a new state as a result of a small change in the input parameters. The effect is irreversible: moving the input parameter back to where it was doesn't get you back to the previous state. The fundamental theorem of catastrophe theory states that, surprisingly, there are only a very small number of ways in which the discontinuous change can happen.

He thinks this is what happens when we find something funny. We have two potential models for our theory, and as we acquire information we initially consider one of the models to be the plausible one. In most cases, we don't even think of the other candidate. Suddenly, we get an extra piece of information: that pushes us over the edge of the cusp, after which the second model immediately becomes the preferred one. Now we see the story differently, and we can't go back to our earlier way of seeing it. He argues, reasonably persuasively, that this explains many of the things we notice about humour, including the importance of timing. If the information is presented in the wrong way, you give away the joke by revealing the second model too soon, and there is no discontinuity.

The book is cooler than you may imagine from reading the above description. He illustrates his ideas with plenty of jokes; also, he is well aware of all the things that might be wrong with his account, and of the fundamental absurdity inherent in trying to reduce humour to mathematics. Indeed, he suggests that you should should think of the book itself as a kind of joke. So read it as a Zen koan whose purpose is to awaken you to a new view of the world which you hadn't previously even considered. It worked on me.